Theme Essential Question: How are sampling of a populations used to make valid inferences and/or predictions about their respective general populations?
Essential Questions:
How can you use a sample to gain information about a population?
How can you use a sample to make and compare predictions about a population?
Standards
7. SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
7. SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
Objectives:
The student will use a sample to gain information about a population.
The student will use a sample to make and compare predictions about a population.
The student will critique the selection process or other possible discrepancies that could affect the outcome of valid predictions.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team (Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 )
In Grade 6, students used measures of center and variability to describe data. Students continue to use this knowledge in Grade 7 as they use random samples to make predictions about an entire population and judge the possible discrepancies of the predictions. Providing opportunities for students to use real-life situations from science and social studies shows the purpose for using random sampling to make inferences about a population.
Make available to students the tools needed to develop the skills and understandings required to produce a representative sample of the general population. One key element of a representative sample is understanding that a random sampling guarantees that each element of the population has an equal opportunity to be selected in the sample. Have students compare the random sample to population, asking questions like ü “Are all the elements of the entire population represented in the sample?” and ü “Are the elements represented proportionally?”
Students can then continue the process of analysis by determining the measures of center and variability to make inferences about the general population based on the analysis. Provide students with random samples from a population, including the statistical measures. Ask students guiding questions to help them make inferences from the sample.
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials athttp://www.azed.gov/educator-certification/
Assessment: Product:
Working with a partner, students will complete one of the following projects and prepare a report:
Part I: Explain the procedure used in the project Part II: Display all chart and graphs used in the project Part III: Using the information provided in the report, draw conclusions
http://illuminations.nctm.org/LessonDetail.aspx?id=L721 In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of “tagged” items to the number of items in a sample is the same as the ratio of tagged items to the total population. or
Use the Gizmo Activities noted below
Key Questions
How is statistics used to gain information about a population by examining a sample of the population?
What must be considered in order to assure the random sample is valid?
How is data used from a random sample draw inferences about the population?
How is the variation in estimations and predictions gauged?
Observable Student Behaviors (Performance)
The student will conduct their own experiment using a sample population in order to make inferences about the general population.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Population Sample Random Sample Biased Sample Prediction
Suggested Activities:
Houghton Mifflin On Core Mathematics Middle School Grade 7
Unit 6-1, p. 139-142
Unit 6-2, p. 143-144
ABC Mastering the Common Core in Mathematics
Chapter 14.8, Simple Random Sampling, p. 185
Chapter 14.9, Representative Sampling, p. 186
Teaching the Common Core Math Standards with Hands-On Activities
Examining Samples (7.SP.1), p. 129-130
How many cubes? (7.SP.2), p. 131-132
Independent computerized lesson
http://www.learner.org/courses/learningmath/data/session9/index.html In this session, you will learn how to use results from a random sample to estimate characteristics of an entire population. To predict the accuracy of your estimates, you will investigate the variation in estimates based on repeated random samples from that population. Highly Recommended: (7.SP.1-2) http://illustrativemathematics.org/illustrations/235, Election Poll, Variation 1 http://illustrativemathematics.org/illustrations/559, Election Poll, Variation 2 http://illustrativemathematics.org/illustrations/558, Election Poll, Variation 3 http://illustrativemathematics.org/illustrations/260, Estimate the mean state area The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
JBHM 8th, GP 3, p. 183-210
Glencoe 7th Grade Mathematics Application and Concepts Course 2,
Chapter 7-3b, p. 301
Chapter 8-3a, p. 344
Chapter 8-3, p. 345-347
Glencoe PreAlgebra, Chapter 6, p. 275
Glencoe Algebra I, Chapter 13-1, p. 708-713
Gizmo Correlation
7.SP.1
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
Polling: Neighborhood
Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.
7.SP.2
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Thinkfinity Links: Search by Common Core Standards/Seventh Grade/Math Often students are confused about ‘where to start’ when solving a multi-step equation. In this lesson the equation is labeled as a ‘party’. The 'host' is labeled (x) with remaining operations being labeled according to their relationship to the host (friends, family, acquaintances, etc...). Technology assignments are used as one method to assess student understanding.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Grade: 7 Unit: 5 Week: 3
Content: Populations and Samples
Generating Multiple Samples
Dates: 3/25/2013 – 3/28/2013 (4 days)
Theme Essential Question:
How are sampling of a populations used to make valid inferences and/or predictions about their respective general populations?
Essential Questions:
Standards
Objectives:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
(Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 )
In Grade 6, students used measures of center and variability to describe data. Students continue to use this knowledge in Grade 7 as they use random samples to make predictions about an entire population and judge the possible discrepancies of the predictions. Providing opportunities for students to use real-life situations from science and social studies shows the purpose for using random sampling to make inferences about a population.
Make available to students the tools needed to develop the skills and understandings required to produce a representative sample of the general population. One key element of a representative sample is understanding that a random sampling guarantees that each element of the population has an equal opportunity to be selected in the sample. Have students compare the random sample to population, asking questions like
ü “Are all the elements of the entire population represented in the sample?” and
ü “Are the elements represented proportionally?”
Students can then continue the process of analysis by determining the measures of center and variability to make inferences about the general population based on the analysis.
Provide students with random samples from a population, including the statistical measures. Ask students guiding questions to help them make inferences from the sample.
Recommended: For a quick overview of the standard(s) to be addressed in this Unit, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Assessment:
Product:
- Working with a partner, students will complete one of the following projects and prepare a report:
Part I: Explain the procedure used in the projectPart II: Display all chart and graphs used in the project
Part III: Using the information provided in the report, draw conclusions
- PBS Activity: Something Fishy
http://www.pbs.org/teachers/mathline/lessonplans/pdf/msmp/somethingfishy.pdfStudents will estimate the size of a large population by applying the concepts of ratio and proportion through the capture-recapture statistical procedure.
or
- Capture-Recapture
http://illuminations.nctm.org/LessonDetail.aspx?id=L721In this lesson, students experience an application of proportion that scientists actually use to solve real-life problems. Students learn how to estimate the size of a total population by taking samples and using proportions. The ratio of “tagged” items to the number of items in a sample is the same as the ratio of tagged items to the total population.
or
Key Questions
Observable Student Behaviors (Performance)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Suggested Activities:
- Houghton Mifflin On Core Mathematics Middle School Grade 7
- Unit 6-1, p. 139-142
- Unit 6-2, p. 143-144
- ABC Mastering the Common Core in Mathematics
- Chapter 14.8, Simple Random Sampling, p. 185
- Chapter 14.9, Representative Sampling, p. 186
- Teaching the Common Core Math Standards with Hands-On Activities
- Examining Samples (7.SP.1), p. 129-130
- How many cubes? (7.SP.2), p. 131-132
- Independent computerized lesson
http://www.learner.org/courses/learningmath/data/session9/index.htmlIn this session, you will learn how to use results from a random sample to estimate characteristics of an entire population. To predict the accuracy of your estimates, you will investigate the variation in estimates based on repeated random samples from that population.
Highly Recommended: (7.SP.1-2)
http://illustrativemathematics.org/illustrations/235,
Election Poll, Variation 1
http://illustrativemathematics.org/illustrations/559,
Election Poll, Variation 2
http://illustrativemathematics.org/illustrations/558,
Election Poll, Variation 3
http://illustrativemathematics.org/illustrations/260,
Estimate the mean state area
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
Videos
SMART Board Lessons, Promethean Lessons
Other Activities, etc.
- http://www.mathgoodies.com/lessons/vol5/division.html
- http://www.math.com/school/subject1/lessons/S1U1L12GL.html
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Activities and tools:
http://www.shodor.org/interactivate/activities/
- Thinkfinity Links: Search by Common Core Standards/Seventh Grade/Math http://www.thinkfinity.org/state-standards-search
- Website tool: http://curvebank.calstatela.edu/circle/circle.htm
- The Area of a Circle-The method of rearranging http://www.themathpage.com/aTrig/area.htm
- Website tools:
http://www.ixl.com/math/grade-5/radius-diameter-circumference-and-area-of-a-circlehttp://curvebank.calstatela.edu/circle/circle.htm
Language
Arts
Week 1
Week 2
Week 3
Week 4
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4